SF Bay Area JI piano tuner (Carl Lumma?)

Hello. I live in San Francisco. Any Bay Area listers here -- (Carl
Lumma, Kevin Grady?) -- who know of piano tuners who can tune my piano
to Just Intonation? What about Bach and other stuff played on the
piano? Tune it back to 12-ET later?

thanks,

Kelly Johnson
chord Explorer

> Hello. I live in San Francisco. Any Bay Area listers here -- (Carl
> Lumma, Kevin Grady?) -- who know of piano tuners who can tune my
> piano to Just Intonation? What about Bach and other stuff played
> on the piano? Tune it back to 12-ET later?

Hi Kelly!

I didn't know you were a fellow Bay Area person. If you mean
Kraig Grady, he's out of LA. I know piano tuners that will
tune your piano in JI, but you might consider doing it yourself.
Unlike ET, JI is very easy to tune (well, depending on what
sort of JI you want)... I could walk you through it.

If you want to go back to ET later, it's no problem, though you
might want to pick a JI scale that's not too far from ET. And
it usually takes 2-3 tunings to really lock in new tuning on a
piano.

-Carl

I know of a few that play with some of the early music groups in the area. I will have to get their contact info. Email me at jrmy@berkeley.edu

On Tue, 13 Sep 2005 03:34:05 -0000
"traktus5" <kj4321@hotmail.com> wrote:
> Hello. I live in San Francisco. Any Bay Area listers here -- (Carl > Lumma, Kevin Grady?) -- who know of piano tuners who can tune my piano > to Just Intonation? What about Bach and other stuff played on the > piano? Tune it back to 12-ET later? > > thanks, > > Kelly Johnson
> chord Explorer
> > > > > > You can configure your subscription by sending an empty email to one
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For an expert, I recommend contacting Eric Siversen, RPT at San Jose
State Univ. Ive attended a few of his lectures on historical piano
topics.
Personally I can tune Wrckmeister by ear, and some other things using
electronic devices.
I tune 7-8 pianos per week, and Im looking to specialize in alternate
tunings.

--- In tuning@yahoogroups.com, "Jeremy Hunt" <jrmy@b...> wrote:
> I know of a few that play with some of the early music groups in the
area. I will have to get
> their contact info. Email me at jrmy@b...
>
>
> On Tue, 13 Sep 2005 03:34:05 -0000
> "traktus5" <kj4321@h...> wrote:
> > Hello. I live in San Francisco. Any Bay Area listers here -- (Carl
> > Lumma, Kevin Grady?) -- who know of piano tuners who can tune my
piano
> > to Just Intonation? What about Bach and other stuff played on the
> > piano? Tune it back to 12-ET later?
> >
> > thanks,
> >
> > Kelly Johnson
> > chord Explorer
> >
> >
> >
> >
> >
> > You can configure your subscription by sending an empty email to one
> > of these addresses (from the address at which you receive the list):
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - leave the group.
> > tuning-nomail@yahoogroups.com - turn off mail from the group.
> > tuning-digest@yahoogroups.com - set group to send daily digests.
> > tuning-normal@yahoogroups.com - set group to send individual emails.
> > tuning-help@yahoogroups.com - receive general help information.
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
> >
> >

One thing you might consider before retuning your piano is how very unsatisfactory is a 12-note fixed rendition of just intonation.

Some electronic keyboards/synthesizers offer a variety of tunings, including JI, to try it out quickly and easily.

The mean-tone and various werkmeisters and others are a different story, they have their own beauty, but just intonation AS A FIXED TEMPERAMENT ON A KEYBOARD locks you to a diatonic framework in a very unsatisfactory way. Very different situation, however, where the tuning can adjust to the harmony.

guglielmo

--- In tuning@yahoogroups.com, Guglielmo <gugliel@g...> wrote:
> One thing you might consider before retuning your piano is how very
> unsatisfactory is a 12-note fixed rendition of just intonation.
>
> Some electronic keyboards/synthesizers offer a variety of tunings,
> including JI, to try it out quickly and easily.
>
> The mean-tone and various werkmeisters and others are a different
story,
> they have their own beauty, but just intonation AS A FIXED TEMPERAMENT
> ON A KEYBOARD locks you to a diatonic framework in a very
unsatisfactory
> way. Very different situation, however, where the tuning can adjust to
> the harmony.
>
> guglielmo

I would second that... unless you positively want to play everything
in F, C and G major and avoid all modulations. Although, there is the
Werckmeister Septenarius (remembering to correct 176 to 175) which is
actually a JI scale, though with no pure thirds.

By JI you would mean pure 5ths and 3rds? Then you really need about 53
notes to the octave.

If you want to pursue a dream of playing known classical music in an
interesting non-equal temperament there are all the temperament
ordinaires etc. and milder circulating temps.

Of course you can use the JI piano to compose your own music, or
indeed just play three-chord rock, for which it is ideal!

~~~T~~~

--- In tuning@yahoogroups.com, Guglielmo <gugliel@g...> wrote:

> One thing you might consider before retuning your piano is how very
> unsatisfactory is a 12-note fixed rendition of just intonation.

I've made that point here probably too many times, but Kelly's case is
different: He's interested in exploring the sound of some JI *chords*
for there own, psychoacoustical and possibly numerological sake,
perhaps as a prelude to actually composing microtonal music.

> but just intonation AS A FIXED TEMPERAMENT
> ON A KEYBOARD locks you to a diatonic framework in a very
unsatisfactory
> way.

I find that just intonation as a fixed temperament on a keyboard
actually prevents me from using the Bach/Beatles diatonic language I'm
accustomed to (with 6 consonant fifths, 7 consonant thirds, 3 major and
3 minor triads that sound nice). However, it can be just right for
certain styles like North Indian improvisation.

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:
> --- In tuning@yahoogroups.com, Guglielmo <gugliel@g...> wrote:
> > One thing you might consider before retuning your piano is how
very
> > unsatisfactory is a 12-note fixed rendition of just intonation.
> >
> > Some electronic keyboards/synthesizers offer a variety of
tunings,
> > including JI, to try it out quickly and easily.
> >
> > The mean-tone and various werkmeisters and others are a different
> story,
> > they have their own beauty, but just intonation AS A FIXED
TEMPERAMENT
> > ON A KEYBOARD locks you to a diatonic framework in a very
> unsatisfactory
> > way. Very different situation, however, where the tuning can
adjust to
> > the harmony.
> >
> > guglielmo
>
>
> I would second that... unless you positively want to play everything
> in F, C and G major and avoid all modulations.

Again, I'd say that even a *single key* (even C major, and certainly
F major and G major) fails to behave appropriately. No need to
modulate to demonstrate the problems.

> Although, there is the
> Werckmeister Septenarius (remembering to correct 176 to 175) which
is
> actually a JI scale, though with no pure thirds.

A high-limit JI scale?

Guglielmo wrote:
> One thing you might consider before retuning your piano is how very > unsatisfactory is a 12-note fixed rendition of just intonation.
> > Some electronic keyboards/synthesizers offer a variety of tunings, > including JI, to try it out quickly and easily.
> > The mean-tone and various werkmeisters and others are a different story, > they have their own beauty, but just intonation AS A FIXED TEMPERAMENT > ON A KEYBOARD locks you to a diatonic framework in a very unsatisfactory > way. Very different situation, however, where the tuning can adjust to > the harmony.
> > guglielmo

The 12-note subset of JI on most keyboards is probably similar to the one on the Yamaha DX7II, which comes in "major" and "minor" varieties (which differ in the tuning of D). It's a bit irregular and can be tricky to work with:

F#--C#--G# F#--C#--G#
\ / \ / \ / \ / \ / \
A---E---B D---A---E---B
/ \ / \ / \ \ / \ / \ /
F---C---G---D F---C---G
\ / \ / \ / \
Eb--Bb Eb--Bb

I prefer a more symmetrical 12-note JI tuning, such as the Ellis Duodene, which has only 3 "wolf" fifths instead of 4:

A---E---B---F#
/ \ / \ / \ /
F---C---G---D
/ \ / \ / \ /
Db--Ab--Eb--Bb

The choice of notes can make a big difference if you're limited to 12 notes per octave, so you might want to try downloading Scala or something like it to try out these scales on a virtual keyboard before committing to a particular one.

http://www.xs4all.nl/~huygensf/scala/

Other possibilities if you're interested in higher limits include Petr Parizek's 12-tone septimal tuning:

! parizek_ji1.scl
!
Petr Parizek, 12-tone septimal tuning, 2002.
12
!
21/20
9/8
7/6
5/4
21/16
7/5
3/2
63/40
5/3
7/4
15/8
2/1

and the "most equal superparticular 12-tone scale" (also from the Scala archive):

! super_12.scl
!
Most equal superparticular 12-tone scale 12
!
16/15
17/15
6/5
19/15
4/3
64/45
68/45
8/5
76/45
16/9
17/9
2/1

None of these work perfectly well in all keys, but they all have their uses.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:

>
> > Although, there is the
> > Werckmeister Septenarius (remembering to correct 176 to 175) which
> is
> > actually a JI scale, though with no pure thirds.
>
> A high-limit JI scale?

Yes, the largest number appearing in the description is 196 (!) - with
the result that it sounds like a moderately unequal circ temp. The
tuning uses the ratios 31 : 39 : 49 : 62 prominently as major thirds.

So it has nothing in common with the audibly just intonation resulting
from 7- or 11- limit, say.

~~~T~~~

This tuning adds little or nothing to to my earlier one http://anaphoria.com/centaur.html this one appears to be the same if you start on F instead of C except mine has a 45/32 instead of a 7/5.
which is an anomaly in the total make up of the scale. you lose your just major for one, and miss having repeated tetrachords

From: Herman Miller <hmiller@IO.COM>

Other possibilities if you're interested in higher limits include Petr Parizek's 12-tone septimal tuning:

! parizek_ji1.scl
!
Petr Parizek, 12-tone septimal tuning, 2002.
12
!
21/20
9/8
7/6
5/4
21/16
7/5
3/2
63/40
5/3
7/4
15/8
2/1

and the "most equal superparticular 12-tone scale" (also from the Scala -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> The 12-note subset of JI on most keyboards is probably similar to
the
> one on the Yamaha DX7II, which comes in "major" and "minor"
varieties
> (which differ in the tuning of D). It's a bit irregular and can be
> tricky to work with:
>
> F#--C#--G# F#--C#--G#
> \ / \ / \ / \ / \ / \
> A---E---B D---A---E---B
> / \ / \ / \ \ / \ / \ /
> F---C---G---D F---C---G
> \ / \ / \ / \
> Eb--Bb Eb--Bb
>
> I prefer a more symmetrical 12-note JI tuning, such as the Ellis
> Duodene, which has only 3 "wolf" fifths instead of 4:
>
> A---E---B---F#
> / \ / \ / \ /
> F---C---G---D
> / \ / \ / \ /
> Db--Ab--Eb--Bb

This was originally proposed by De Caus. Somtimes, it's preferable
still to use Marpurg's Monochord #1, which also has 12 good triads
(as usual, one reading the list on yahoo has to click on "reply" to
view this correctly):

C#--G#
/ \ / \
A---E---B---F#
/ \ / \ / \ /
F---C---G---D
\ / \ /
Eb--Bb

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> > --- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:
>
> >
> > > Although, there is the
> > > Werckmeister Septenarius (remembering to correct 176 to 175)
which
> > is
> > > actually a JI scale, though with no pure thirds.
> >
> > A high-limit JI scale?
>
> Yes, the largest number appearing in the description is 196 (!)

196 = 2*2*7*7, so there's nothing inherently high-limit about that.

> - with
> the result that it sounds like a moderately unequal circ temp. The
> tuning uses the ratios 31 : 39 : 49 : 62 prominently as major >
thirds.

Aha. Is 31 the highest prime in the tuning? Monz would like to know :)

> So it has nothing in common with the audibly just intonation
>resulting
> from 7- or 11- limit, say.

Understood -- it's better described as "tempering with ratios,"
right? Johnny showed me a Kirnberger book and asked me why he used
ratios of 161 -- the answer is a rational splitting of the syntonic
comma, 81/80 or 162/160, into two parts, 162/161 and 161/160. These
kinds of specifications were very common when string lengths were
still used to specify tunings and logarithms of any kind were still
very new.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> (as usual, one reading the list on yahoo has to click on "reply" to
> view this correctly):

Apparently that depends on the computer setup; on the computer I'm
looking at now, it's fine.

Kraig Grady wrote:
> This tuning adds little or nothing to to my earlier one > http://anaphoria.com/centaur.html > > this one appears to be the same if you start on F instead of C except mine
> has a 45/32 instead of a 7/5.
> which is an anomaly in the total make up of the scale. you lose your just
> major for one, and miss having repeated tetrachords

They're different sorts of scales, really. Centaur adds 7-limit intervals to the diatonic scale, while Parizek's scale is a regular 3x2x2 array.

Centaur
5/3---5/4--15/8
/ \ / \ / \
14/9-7/6---7/4\ / \
4/3--\1/1/-\3/2---9/8
\ / \
7/5--21/20

Parizek
5/3---5/4--15/8
\ / \ / \
7/6---7/4--21/16
\1/1/-\3/2/-\9/8
\ / \ / \
7/5--21/20-63/40

I'd like to think that a scale like this must have been known before 2002, but that's the one that I found in the Scala archive when I was looking for this particular scale a while back.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> > > > Although, there is the
> > > > Werckmeister Septenarius (remembering to correct 176 to 175)
> which
> > > is
> > > > actually a JI scale, though with no pure thirds.
> > >
> > > A high-limit JI scale?
> >
> > Yes, the largest number appearing in the description is 196 (!)
>
> 196 = 2*2*7*7, so there's nothing inherently high-limit about that.
>
> > - with
> > the result that it sounds like a moderately unequal circ temp. The
> > tuning uses the ratios 31 : 39 : 49 : 62 prominently as major >
> thirds.
>
> Aha. Is 31 the highest prime in the tuning? Monz would like to know :)
>
> > So it has nothing in common with the audibly just intonation
> >resulting
> > from 7- or 11- limit, say.
>
> Understood -- it's better described as "tempering with ratios,"
> right? Johnny showed me a Kirnberger book and asked me why he used
> ratios of 161 -- the answer is a rational splitting of the syntonic
> comma, 81/80 or 162/160, into two parts, 162/161 and 161/160. These
> kinds of specifications were very common when string lengths were
> still used to specify tunings and logarithms of any kind were still
> very new.

I believe Faulhaber (in an engineering textbook!) used logs in 1630 to
come very close to 12tet, but among musicians I agree, logs were not
common.

The Werckmeister string length numbers are:

196 186 175 (corrected from 176) 165 156 139 131 124 117 110 104 98

of which the largest prime is 139, partnered with 186 and 110 in the
division of an octave into three thirds. I'm sure Monz knows about it
already, although the Tonalsoft page
http://tonalsoft.com/enc/w/werckmeister.aspx only gives two out of
Werckmeister's four explicitly described 'good' tunings.

~~~T~~~

This scale has more features than that as my page on it testifies.
both have two harmonic pentads , but why would you want them where they are in the latter case.
a tritone apart. i recommend going through all the keys and really looking at the scale.
A good alternative to my is the one developed by David Canright, which extends the limit over the two series a fifth apart.
Date: Thu, 15 Sep 2005 23:22:44 -0500
From: Herman Miller <hmiller@IO.COM>
Subject: Re: Re: SF Bay Area JI piano tuner (Carl Lumma?)

They're different sorts of scales, really. Centaur adds 7-limit intervals to the diatonic scale, while Parizek's scale is a regular 3x2x2 array.

Centaur
5/3---5/4--15/8
/ \ / \ / \
14/9-7/6---7/4\ / \
4/3--\1/1/-\3/2---9/8
\ / \
7/5--21/20

Parizek
5/3---5/4--15/8
\ / \ / \
7/6---7/4--21/16
\1/1/-\3/2/-\9/8
\ / \ / \
7/5--21/20-63/40

I'd like to think that a scale like this must have been known before 2002, but that's the one that I found in the Scala archive when I was looking for this particular scale a while back.

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

> This scale has more features than that as my page on it testifies.
> both have two harmonic pentads , but why would you want them where >
they are in the latter case. a tritone apart.

It looks like Parizek's scale has only 1 harmonic (otonal) pentad,
while yours has 2. Am I seeing that wrong?

There are a lot of 12-tone 7-limit scales that were discussed back
around the time the present list archive begins. I'm not sure if Herman
was here yet (?)

>i recommend going through all the keys and
>really looking at the scale.

A lot of pairs of similar tetrachords in yours, the importance of which
I've tried to emphasize with concepts like "omnitetrachordality". What
else do you find?

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> There are a lot of 12-tone 7-limit scales that were discussed back
> around the time the present list archive begins. I'm not sure if
Herman
> was here yet (?)

And since.

In this diagram, taken from recent messages, is there a name for the ROWS (or, getting familiar with the style of this list, are there many conflicting names :) ? The C#-G# row, the A-E-B-F# row, the F-C-G-D and the Eb-Bb row?

> > C#--G#
> / \ / \
> A---E---B---F#
> / \ / \ / \ /
> F---C---G---D
> \ / \ /
> Eb--Bb
> > Thanks!

Guglielmo

wallyesterpaulrus wrote:
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> > >>This scale has more features than that as my page on it testifies.
>> both have two harmonic pentads , but why would you want them where > > > they are in the latter case. a tritone apart.
> > It looks like Parizek's scale has only 1 harmonic (otonal) pentad, > while yours has 2. Am I seeing that wrong?
> > There are a lot of 12-tone 7-limit scales that were discussed back > around the time the present list archive begins. I'm not sure if Herman > was here yet (?)

I'm sure there are plenty of 12-tone 7-limit scales; I just mentioned one of them. You could move any of these notes around by commas and come up with a bunch of different scales, and many of them would have advantages in one area or another. The point is that the built-in "JI" tunings of synthesizers aren't the only or even necessarily the best scales to start out with; there are plenty of alternatives that are worth looking into before doing something as time consuming as having a piano retuned. (I'd actually go with one of the 19-limit scales myself, but all of these scales have their own individual flavors that can suggest different musical ideas.)

It's possible that the original poster had a specific JI scale in mind, but I was replying to Guglielmo's comment that "just intonation as a fixed temperament on a keyboard locks you to a diatonic framework in a very unsatisfactory way." I just wanted to mention a few scales that I've found to be more or less "satisfactory" (and to illustrate that the scales need not be "diatonic").

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> Hello. I live in San Francisco. Any Bay Area listers here -- (Carl
> Lumma, Kevin Grady?) -- who know of piano tuners who can tune my
piano
> to Just Intonation? What about Bach and other stuff played on the
> piano? Tune it back to 12-ET later?
>
> thanks,
>
> Kelly Johnson
> chord Explorer

Sorry to be so 'tardy' getting to this.

John Allair, in Petaluma (I believe), told me when he was doing my
piano that if I wanted any of the Jorgenson tunings, or JI, or Partch
(!) or whatever, he'd fire it up for me, for a nominal fee :-) of
course. I liked him, and he did a good a job on my old (converted
player) Story and Clark.

I'm pretty sure you can find him, but I don't know if he still roams
the Bay Area tuning pianos for people. Even very recently he was
doing gigs with his R & B band around Sonoma County. From what I
gather, he's a hell of a B3 player, too!

Cheers,

Pete

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> I'm sure there are plenty of 12-tone 7-limit scales; I just
mentioned
> one of them.

To add to the fun, there are 12-tone 7-limit tempered scales where
the tempering is considerably more accurate than meantone, in the
near-JI range. The most expeditious way to do this is to marvel
temper; that is, to get the 7-limit from a 5-limit starting point by
tempering out 225/224. And example would be the 12-note scale
obtained by marvel tempering the Ellis duodene, which is one of the
class of scales I've called "marvelous dwarves".

While most attention has been focused either on JI or on scales with
two generators, the range in between, and three generator ("planar")
tempered scales in particular, are quite useful for scale
construction.

> It's possible that the original poster had a specific JI scale in
mind,
> but I was replying to Guglielmo's comment that "just intonation as
a
> fixed temperament on a keyboard locks you to a diatonic framework
in a
> very unsatisfactory way."

If you assume "diatonic" entails meantone, you could argue it locks
you *out* of a diatonic framework.

--- In tuning@yahoogroups.com, Guglielmo <gugliel@g...> wrote:

> In this diagram, taken from recent messages, is there a name for the
> ROWS (or, getting familiar with the style of this list, are there
many
> conflicting names :) ? The C#-G# row, the A-E-B-F# row, the F-C-G-D
and
> the Eb-Bb row?

You could call it "the chain of fifths from C", etc. Of course, if you
start referring to "the chain of fifths from C#" in a 5-limit context,
it raises the question of what, exactly, C# means. "The chain of fifths
from 25/24" might be better.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> wallyesterpaulrus wrote:
> > --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...>
wrote:
> >
> >
> >>This scale has more features than that as my page on it testifies.
> >> both have two harmonic pentads , but why would you want them
where >
> >
> > they are in the latter case. a tritone apart.
> >
> > It looks like Parizek's scale has only 1 harmonic (otonal)
pentad,
> > while yours has 2. Am I seeing that wrong?
> >
> > There are a lot of 12-tone 7-limit scales that were discussed
back
> > around the time the present list archive begins. I'm not sure if
Herman
> > was here yet (?)
>
> I'm sure there are plenty of 12-tone 7-limit scales; I just
mentioned
> one of them. You could move any of these notes around by commas and
come
> up with a bunch of different scales, and many of them would have
> advantages in one area or another. The point is that the built-
in "JI"
> tunings of synthesizers aren't the only or even necessarily the
best
> scales to start out with; there are plenty of alternatives that are
> worth looking into before doing something as time consuming as
having a
> piano retuned. (I'd actually go with one of the 19-limit scales
myself,
> but all of these scales have their own individual flavors that can
> suggest different musical ideas.)
>
> It's possible that the original poster had a specific JI scale in
mind,
> but I was replying to Guglielmo's comment that "just intonation as
a
> fixed temperament on a keyboard locks you to a diatonic framework
in a
> very unsatisfactory way." I just wanted to mention a few scales
that
> I've found to be more or less "satisfactory" (and to illustrate
that the
> scales need not be "diatonic").

The original poster made mention of chords with primes as high as 13
on the harmonic entropy list -- perhaps one of the 12-note 13-limit
tunings (Dave Canright's or others) might be best for him.

on 9/19/05 12:34 PM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

> The original poster made mention of chords with primes as high as 13
> on the harmonic entropy list -- perhaps one of the 12-note 13-limit
> tunings (Dave Canright's or others) might be best for him.

Personally I like the following scale (don't know if it has a name) which
has the 11 and 13 in two keys (in this case C and G):

>C# D D# E F F# G G# A A# B
>
>33/32 9/8 39/32 5/4 21/16 11/8 3/2 13/8 27/16 7/4 15/8

I like this better than Canright's scale, which, if I've got it right, only
has the 11-limit in one key rather than two.

One way of saying it is that each scale has the harmonic series through 15
in two keys with one omission. Canright's has 11 missing in one key,
whereas the scale above has 15 missing in one key.

I really like having the 11 and 13 available in both keys, and have left
this tuning on my harpsichord for many months.

However, I actually use a hybrid of 2 tunings on my harpsichord. In the
treble I use the tuning above. In the bass, I find the 11 and 13 are not
useful, and so I reuse these notes (C# D# F# G#) in a way that makes the
tuning closer to Duodene. There are a lot of possible variations, but the
general idea of discarding harmonics 11 and 13 from the lower register is I
believe quite useful if you can keep track of it since it opens up the
5-limit modulation possibilities a bit.

Kelly, if you end up putting a tuning like this on your piano, keep in mind
that the the "11" pitches will be around a half-semitone sharp of equal
temperament. Maybe that is something you'd want to be careful about with
piano strings, if the piano is of any value. You could work around it by
flatting the whole scale a bit, but maybe even that poses some risk if you
later bring the tuning back closer to ET, I don't know.

Whatever just tuning you get put on your piano, I hope you let us know when
it is done, and invite all the locals over to hear it!

-Kurt

I likewise had mentioned Canwrights 12 tone scales as excellent 12 tone tunings

From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
Subject: Re: SF Bay Area JI piano tuner (Carl Lumma?)

The original poster made mention of chords with primes as high as 13 on the harmonic entropy list -- perhaps one of the 12-note 13-limit tunings (Dave Canright's or others) might be best for him.

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

I mentioned them before either of you -- big whoop.

-Carl

>> I likewise had mentioned Canwrights 12 tone scales as excellent 12
>> tone tunings
>
> The original poster made mention of chords with primes as high as 13
> on the harmonic entropy list -- perhaps one of the 12-note 13-limit
> tunings (Dave Canright's or others) might be best for him.

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 9/19/05 12:34 PM, wallyesterpaulrus <wallyesterpaulrus@y...>
wrote:
>
> > The original poster made mention of chords with primes as high as
13
> > on the harmonic entropy list -- perhaps one of the 12-note 13-
limit
> > tunings (Dave Canright's or others) might be best for him.
>
> Personally I like the following scale (don't know if it has a name)
which
> has the 11 and 13 in two keys (in this case C and G):
>
> >C# D D# E F F# G G# A A# B
> >
> >33/32 9/8 39/32 5/4 21/16 11/8 3/2 13/8 27/16 7/4 15/8
> ...
> Kelly, if you end up putting a tuning like this on your piano, keep
in mind
> that the the "11" pitches will be around a half-semitone sharp of
equal
> temperament.

Not so: The "11" pitches would be ~1/2-semitone low. It's the "13"
pitches that will be higher by about 4/10 semitone.

> Maybe that is something you'd want to be careful about with
> piano strings, if the piano is of any value. You could work around
it by
> flatting the whole scale a bit, but maybe even that poses some risk
if you
> later bring the tuning back closer to ET, I don't know.

Two considerations:

1) Total tension on the frame -- not a problem, since the increase in
tension for the 13's would be compensated for by the reduction in
tension for the 11's.

2) Increased tension on the individual "13" strings.

--George

> Two considerations:
>
> 1) Total tension on the frame -- not a problem, since the increase
> in tension for the 13's would be compensated for by the reduction
> in tension for the 11's.

As Canright points out, total tension concerns can be mitigated by
adding the mean deviation from 12-tET to every pitch class in the
new scale before tuning. I have used this approach with good
results.

-Carl

on 9/20/05 10:03 AM, George D. Secor <gdsecor@yahoo.com> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>> on 9/19/05 12:34 PM, wallyesterpaulrus <wallyesterpaulrus@y...>
> wrote:
>>
>>> The original poster made mention of chords with primes as high as
> 13
>>> on the harmonic entropy list -- perhaps one of the 12-note 13-
> limit
>>> tunings (Dave Canright's or others) might be best for him.
>>
>> Personally I like the following scale (don't know if it has a name)
> which
>> has the 11 and 13 in two keys (in this case C and G):
>>
>>> C# D D# E F F# G G# A A# B
>>>
>>> 33/32 9/8 39/32 5/4 21/16 11/8 3/2 13/8 27/16 7/4 15/8
>> ...
>> Kelly, if you end up putting a tuning like this on your piano, keep
> in mind
>> that the the "11" pitches will be around a half-semitone sharp of
> equal
>> temperament.
>
> Not so: The "11" pitches would be ~1/2-semitone low. It's the "13"
> pitches that will be higher by about 4/10 semitone.

Oops, right! Glad you caught that.

-Kurt

>> The original poster made mention of chords with primes
>> as high as 13 on the harmonic entropy list -- perhaps one
>> of the 12-note 13-limit tunings (Dave Canright's or others)
>> might be best for him.
>
> Personally I like the following scale (don't know if it has
> a name) which has the 11 and 13 in two keys (in this case C
> and G):
>
> >C# D D# E F F# G G# A A# B
> >
> >33/32 9/8 39/32 5/4 21/16 11/8 3/2 13/8 27/16 7/4 15/8
>
> I like this better than Canright's scale, which, if I've got it
> right, only has the 11-limit in one key rather than two.

Nope, this is Canright's scale (...

13/12
9/8
7/6
5/4
4/3
11/8
3/2
13/8
5/3
7/4
11/6
2/1

...) with 4/3 mapped to C. It was me who preferred to drop
the 11 of the lower series (11/6) in favor of the more 5-limit
fifths and thirds (15/8).

-Carl